There is open-source Matlab code, by Prof. Sigmund. www.topopt.mek.dtu.dk/apps-and-software/a-99-line-topology-optimization-code-written-in-matlab (The interactive App was developed with Unity3D.)
who else was sad that no Lego got used in this video? would love to see the actual physical proof that the topology worked, and not just a few low resolution diagrams, great job at explaining topology, but very poor job at showing it
Missing a few constraints that you’ll improve the AI. Rather than size… consider maximum space constraints. New input factor: material. Allow the AI to choose the material from the global database. New input factor: Constraints = temperature, durability, radioactivity, chemical interactivity, etc. New input factor: cost. Give it a budget for material costs to create material optimization using the above constraints. New input factor: light/shadow requirements (Eg under a bridge, etc.). Allow reflection and bounce. New secondary input factor: beauty and/or symmetry. Program phi, symmetry, balance, prior artistic understanding of beauty, and current human sample populations of polls for training. Attempt the primary design both without and with this optional/secondary input factor.
great work , please can You recommend great book to learn TO from scratch im new in this field .. my first year in phd (Topology optimization for additive manufacturing) what i should learn first please help me
Hello sir, I am a master’s student and I am researching this topic topology optimization and I need your help and your lectures regarding the topic in pdf format. Thank you in advance
What do you mean when you relax the design variables to be continuous? Does it mean the design variables can be anywhere within 1 to 0, which means there will be a density gradient? Also I am currently undertaking a project that seeks to apply topology optimisation for lattice structures, do you have any research papers you recommend for a person with zero prior no knowledge like me. Thanks
yes, relaxation refers to allowing the design variables to be anywhere within [0,1]. In compliance minimization which is the case in my example, you get a pretty black and white design, meaning that most density values are very close to 1 or 0. In some special cases, e.g, if you have a distributed load, it is likely that there is a visible density gradient. For getting multi-scale structures, I recommend our review article on this topic homepage.tudelft.nl/z0s1z/projects/2021-multiscale-review.html
Nice video ! As I know that Simp is the most common method in TO, I 've read some documentation about it but still don't understand how it deals with gray elements (with density between 0 and 1). Please explain it in more detail, and try to tie this to the schematic diagram you showed in video. I am new to this field, so I really want to get your explainations, or some related documents. Thank you !
Good question, Xuân If the density of an element is zero, apparently its stiffness shall be zero. If its density is one, let's say its stiffness is 1E. For intermediate densities we need to an interpolation function to get their stiffness. The first idea one may come up with is to use a linear interpolation. Then a density of 0.5 leads to a stiffness of 0.5E. However, it is known that if the ratio of solid material in a microstructure volume is 50%, theoretically its stiffness is lower than 0.5E. This is known as Hashin-Shtrikman bounds. For a solid material with a Poisson's ratio 0.3, this theoretical bound can be approximated by a cubic function. Thus comes the popular power law interpolation with a power of 3 (also referred to as the penalization parameter). Under this physically realistic interpolation, since with 0.5 material one gets less than 0.5E stiffness, it is not economical to use 0.5 material, and thus the optimization automatically converges to a solution with densities either close to zero or close to one, i.e., a binary design. I suggest to download the popular 99 or 88 line topopt code, and play with the 'penal' value to see the effects.
So Simp method solves the gray elements by calculating its density value. Through iterations, these intermediate density values will gradually progress to the value 0 or 1. Am I correct in this ? If Yes, then I have 2 assumptions about determining the density value of the element: 1 : Initial density value before iteration of the element is determined based on calculating its displacement (corresponding to steps 1 and 2 in your diagram), then the density value will change through iterations in the direction towards 0 or 1. However, I have not found any relationship between the displacement of an element and its density value. If this is true can you show it ? 2 : The initial density value of an element is randomly determined, and the change of this value through the iterations is also random. The structural displacement (or stiffness) formula is just to compare how the element's contribution to the overall stiffness changes as its density value changes. If the contribution is small then the element will be removed and vice versa. This is consistent with your interpretation of sensitivity. But if this is true, is the statement "is the density value of the element really approaching 0 or 1" guaranteed ? Or the change of density value is no rule at all ? I find this to be a very interesting field, but there is still a lot to understand about it. Looking forward to hearing more from you. Thanks very much
Dear sir I have some questions For a program like Ansys does it perform the sensitivity analysis under the hood? If no how can one perform a sensitivity analysis? Does it have to be done after validation? What are the variable that can be changed for truss optimisation problem? What do you mean by density as variable? Thanks in advance
Many CAE programs such as Ansys and Solidworks provide the functionality of topology optimization. I would be very surprised if they don't perform sensitivity analysis in optimization. "What are the variable that can be changed for truss optimisation problem?" In truss optimization, the design variable is typically the radius. When the radius becomes zero (or a very small value), it means that the corresponding truss is not needed. "What do you mean by density as variable?" I meant a pseudodensity, not the physical density of the material. The pseudodensity (0 or 1) indicates whether there is material at the element.
Thank you very much for sharing your beautiful work. I wish you success and happiness in life. If you may; I have a simple question: Do you know of any good references for applying SIMP Topological Optimization method in 3D? Also, in your opinion.. do you think it is of academic value to actually design and solve code/algorithms for solving topological optimization problems? Or are we better off just using available software and focusing on other issues within the studied problem? I'm trying to design a compliant mechanism optimized for strength and flexibility in three dimensions. Thanks again for sharing.
SIMP in 3D appears in many works. The challenge is computational efficiency. Matlab: An efficient 3D topology optimization code written in Matlab Kai Liu & Andrés Tovar A new generation 99 line Matlab code for compliance topology optimization and its extension to 3D F Ferrari, O Sigmund GPU: A System for High-Resolution Topology Optimization Jun Wu, Christian Dick, and Rüdiger Westermann HPC Topology optimization using PETSc: An easy-to-use, fully parallel, open source topology optimization framework N Aage, E Andreassen, BS Lazarov "a compliant mechanism optimized for strength and flexibility in three dimensions" You may want to check this work. Topology optimization of compliant mechanisms considering stress constraints, manufacturing uncertainty and geometric nonlinearity GA da Silva, AT Beck, O Sigmund There are many open questions in topology optimization and its application in various domains. It is definitely of high academic value to investigate it.
The plug-in can be downloaded here. It was developed a few years ago, and some changes may be necessary for the latest version of Grasshopper. www.dropbox.com/s/zbh3mg26zscqa32/InfillOpt.zip?dl=0 Alternatively, I strongly suggest to use the Matlab version. Code available at homepage.tudelft.nl/z0s1z/projects/2017-bone-infill.html
Thank you so much for sharing such a wonderful introduction about topology optimization! Actually, I am also green hands in this field. What recently annoys me is that the result of topology optimization contains too many small characters, such as thousands of tiny facets (the output file is in form of a .stl file). And that brings low-quality mesh when I want to further simulate its performance with FEM in different situations. Should I smooth the surface? How to reduce the result's characters properly?
I'm not sure what kind of mesh you got. If the optimization is performed on a decent resolution using voxels, the mesh constructed by the marching cubes algorithm shall not be too irregular. There might be staircase artifacts, but can be smoothed by post-processing, such as Taubin smoothing (available in e.g. MeshLab). If the mesh is rather coarse, a smoothing operator may change the shape substantially. One could play with different smoothing algorithms. The smoothed geometry likely does not conform with the boundary conditions, so some manual adjustment could be necessary.
Hi Jun Wu, Amesome work by the way . I use topology optimization tools available in some commercial softwares , would love to learn the maths behind it .. It would be helpful if it is possible for you to share the mathematical equations you had used for this optimization. A basic formulation of the stiffness matrix and so on.. If Some kind of a detailed documentation is available with you .. If so could you share it to my personal Email ID : aadithyasathya94@gmail.com ... Many thanks
Thanks for your interest. I recommend the 99-line topopt paper by Prof. Sigmund at DTU Denmark, www.topopt.mek.dtu.dk/Apps-and-software/A-99-line-topology-optimization-code-written-in-MATLAB Here the equations are explained.
Great suggestion! Stress constraints have been a topic of interest in topology optimization since late 1990s. There are a number of recent developments. I hope to share some results soon.
Okay great, also when i read the literature about stress constraints in topology optimization, they use aggregating techniques like p norm or ks function. I have already perform the stress constraints topology optimization under minimise volume objective function in Ansys using simp technique, but now i want to validate my Ansys results with the stress constraints imposition techniques used in literature. It is really a great help if you make a small demonstration that how to impose global stress constraints using p norm or ks function.
This is some really great work Prof. Jun Wu, and I would love to use the plug in if its possible. I'm working on a variable infill project, and your videos were absolutely beneficial. Please recommend me some papers and books that I can get some theoretical background. As my background is more into Electronics and robotics, but I'm working on a similar project right now. Thanks a lot!
Sorry for a late reply. I hope our recent review article on multi-scale topology optimization will be helpful to you. homepage.tudelft.nl/z0s1z/projects/2021-multiscale-review.html
The code for infill optimization can be downloaded from this page, just in case if you have missed it homepage.tudelft.nl/z0s1z/projects/2017-bone-infill.html This shall provide a good basis for implementing the shell-infill approach. Re-implementation of this approach, with some interesting adaptations, can be seen in a number of recent papers.
I wonder if this " infillopt* " software has been published ,I am a student and very interested in your study, and I am also researching algorithm like this. Could you give me some advice and help
sorry for a late reply. If it still helps, and in case you have missed it, the code for infill optimization can be downloaded homepage.tudelft.nl/z0s1z/projects/2017-bone-infill.html
